UPTEC ES08 007 Examensarbete 20 p Mars 2008 Modelling and control of a district heating system Linn Saarinen
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UPTEC ES08 007
Examensarbete 20 pMars 2008
Modelling and control of a district heating system
Linn Saarinen
Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student
Abstract
Modelling and control of a district heating system
Linn Saarinen
The aim of this study was to investigate whether the supply temperature to a districtheating system could be decreased if a dynamic model of the system is used todetermine the supply temperature control point, and to what extent the decrease ofthe supply temperature would improve the electricity efficiency of the connectedcombined heat and power plant. This was done by a case study of the district heatingsystem of Nyköping and its 58 MW heat and 35 MW electricity CHP plant. Thedistrict heating network was approximated as a point load with a variable time delay.Prediction models of the heat load, return temperature and transport time of thesystem were estimated from operational data of the heat plant. The heat load wasmodelled with an ARX model using the 24 hour difference of the outdoortemperature as input signal and the 24 hour difference of the load as output signal. Acomparison between using a regular control curve and using the dynamic model forcontrolling the supply temperature indicated that with the same risk of heat deficit,the dynamic control strategy could increase the electricity production with 390 MWhper year, most of it during the winter months. This would correspond to an increasedannual income of about 200 000 SEK for the owner.
Sponsor: Vattenfall Research and DevelopmentISSN: 1650-8300, UPTEC ES08 007Examinator: Ulla TengbladÄmnesgranskare: Bengt CarlssonHandledare: Andreas Lennartsson
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Sammanfattning
Fjärrvärmenät finns i de flesta större samhällen i Sverige. I ett eller flera centrala värmeverk
förbränns exempelvis skogsflis, avfall eller torv och värmen distribueras via ett isolerat
vattenledningsnät till kunder runt om i samhället, som växlar över värme från fjärrvärmenätet
till sina egna radiator- och varmvattensystem. I vissa fall har värmeverket också en ångturbin
för elproduktion, och kallas då kraftvärmeverk. Värmen från förbränningen i pannan värmer
vatten till ånga, som får passera ångturbinen och därefter kyls av fjärrvärmenätets vatten.
Elproduktionen från en ångturbin beror av skillnaden mellan temperaturen på ångan före och
efter turbinen. För att få en hög elproduktion vill man alltså ha en låg temperatur efter
turbinen. Å andra sidan ställer värmebehovet på fjärrvärmenätet krav på att temperaturen inte
får vara för låg, för ju lägre temperaturen på fjärrvärmevattnet blir, desto mindre värme per
kubikmeter vatten transporteras från värmeverket till kunden. Vanligen styrs
framledningstemperaturen (temperaturen på vattnet som skickas ut på fjärrvärmenätet från
värmeverket) av utomhustemperaturen. När det är kallt ute behöver ju kunderna mer värme.
Sedan systemet med gröna elcertifikat infördes i Sverige har elproduktion på biobränsleeldade
kraftvärmeverk blivit mycket lönsam. Detta har gett incitament till industrin att konvertera
värmeverk till kraftvärmeverk och även att höja elproduktionen på befintliga anläggningar.
Problemet om man vill höja elproduktionen på ett kraftvärmeverk är att för en viss mängd
producerad el produceras också en större mängd värme. Därför är elproduktionen beroende av
efterfrågan på värme. I Nyköping har man till exempel börjat kyla bort värme från
returledningen för att kunna öka elproduktionen på kraftvärmeverket vid tidpunkter då
efterfrågan på värme är låg men elpriserna höga. Att sänka framledningstemperaturen innebär
att man ökar andelen producerad el jämfört med producerad värme, och skulle kunna vara en
billigare och mer energieffektiv metod att öka elproduktionen. I denna studie har en modell
för värmebehovet och dynamiken på fjärrvärmenätet tagits fram för att kunna styra
framledningstemperaturen mer precist. Exempelvis tar modellen hänsyn till att värmebehovet
följer ett speciellt dygnsmönster som beror av kundernas beteende – som att mest varmvatten
används under morgontimmarna. Med hjälp av driftdata från kraftvärmeverket i Nyköping har
en modell skattats som både använder mätningar av utomhustemperaturen och beräkningar av
värmeförbrukningen några timmar tillbaka för att förutsäga vilket värmebehovet kommer att
bli de närmaste timmarna, och därigenom vilken framledningstemperatur som krävs. Detta
innebär att framledningstemperaturen kan sänkas när värmebehovet inte är så stort, och då
pressas verkningsgraden på elproduktionen upp. Resultaten av den här studien indikerar att
elproduktionen på kraftvärmeverket i Nyköping skulle kunna höjas med omkring 390 MWh
per år utan att värmeproduktionen ökas, vilket skulle innebära cirka 200 000 kr i ökade
intäkter för ägaren Vattenfall.
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Acknowledgements
I would like to express my gratitude to the people who have given me their time and support
during this degree project. First of all, thanks to my supervisor Andreas Lennartsson at
Vattenfall and my examiner Bengt Carlsson at Uppsala University, who have given me
feedback and good discussions. A special thanks also to Katarina Boman and Jozef Nieznaj at
Vattenfall, for their help and answers to my numerous questions. And finally, thanks to all the
other people at Vattenfall who have taken an interest in my project and assisted me in
different ways, among them Christer Andersson, Majjid Mohammadi, Anna Helgesson, Rolf
Abrahamsson and Peter Herbert.
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Contents Abstract.......................................................................................................................................1
Sammanfattning ......................................................................................................................... 2
Acknowledgements .................................................................................................................... 3 Contents ...................................................................................................................................... 4 1 Introduction ............................................................................................................................. 6
1.1 Motivations ....................................................................................................................... 6 1.2 Methods ............................................................................................................................ 6
1.3 This report ........................................................................................................................ 7 2 Theory ..................................................................................................................................... 8
2.1 District heating ................................................................................................................. 8 2.2 Supply temperature and electricity output........................................................................ 9 2.3 Dynamics of district heating networks ........................................................................... 10
2.3.1 Time delays ............................................................................................................. 10
2.3.2 Loading/unloading the system ................................................................................ 10 2.3.3 Calculation of the heat load ..................................................................................... 11
2.3.4 Heat load models ..................................................................................................... 12 2.3.5 Dynamics of the return temperature ........................................................................ 12
2.4 Feed forward control ...................................................................................................... 13 2.5 Empirical modelling ....................................................................................................... 14
2.5.1 The ARX model ...................................................................................................... 15 2.5.2 Prediction with the ARX model .............................................................................. 16
2.5.3 Time dependent variations ...................................................................................... 18 2.6 Previous research ............................................................................................................ 18
3 Case study ........................................................................................................................ 21
3.1 Idbäcken’s CHP-plant .................................................................................................... 21 3.2 The district heating network of Nyköping ..................................................................... 22
3.3 Electricity output and supply/return temperature ........................................................... 23 3.4 Maximal flow on the DH network ................................................................................. 26
3.5 Load and return temperature characteristics .................................................................. 28 4 Modelling of the heat load .................................................................................................... 30
4.1 A static model ................................................................................................................. 30 4.2 Dynamic model .............................................................................................................. 33
4.2.1 Calculation of previous load ................................................................................... 34 4.2.2 Time delays and prediction horizon ........................................................................ 35 4.2.3 Load model .............................................................................................................. 35 4.2.4 Result of the dynamic modelling ............................................................................ 39
4.3 Comparison of the static and dynamic model ................................................................ 41
4.4 Return temperature model .............................................................................................. 41 5 Control strategies ................................................................................................................... 43
5.1 Calculation of control point for the supply temperature ................................................ 44
5.2 Comparison with the present control strategy ................................................................ 45 5.2.1 High load case ......................................................................................................... 45 5.2.2 Medium load case .................................................................................................... 47 5.2.3 Long term comparison ............................................................................................ 49
5.3 Economy ......................................................................................................................... 52 5.4 Implementation ............................................................................................................... 53
6 Discussion ............................................................................................................................. 54
6.1 Input signals ................................................................................................................... 54
5
6.2 Possible improvements ................................................................................................... 54
6.3 Drawbacks and benefits.................................................................................................. 55 7 References ............................................................................................................................. 56
7.1 Litterature ....................................................................................................................... 56
7.2 Data ................................................................................................................................ 57 7.3 Other ............................................................................................................................... 57
Appendix 1: The simulink model A1
Appendix 2: Matlab functions for calculation of transport times k, l and lhat A7
Appendix 3: Matlab functions for load prediction A9
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1 Introduction
The objective of this master’s degree project is to investigate the possibility to increase the
electricity efficiency of the combined heat and power plant Idbäcken in Nyköping by
decreasing the supply temperature to the district heating system. The decrease of the supply
temperature should be made possible by applying a dynamic control strategy for the supply
temperature, using a dynamic model of the district heating system. The reliability of the heat
distribution to the customers must not be compromised.
1.1 Motivations
District heating is a well spread technology in Sweden. Most cities have heat plants and
infrastructure for district heating, and the customers are of many kinds; households, offices,
shops, industry etc. The heat plants use a wide range of fuels. Renewables such as wood
chips, pellets and waste materials are common, together with peat, municipal waste and
electricity used in heat pumps. Waste heat from industrial processes is also used at locations
where such energy is available. Some heat plants have a steam turbine and co-produce heat
and electricity. After the system of green certificates for electricity was initiated in Sweden
2003, the electricity production from such combined heat and power (CHP) plants has
become quite lucrative. The incitement for building CHP plants rather than heat plants has
thereby increased, as well as the incitement for increasing the electricity production in already
existing plants.
The electricity production from thermal energy is subject to the laws of thermodynamics.
Since the exergy (or energy quality) of thermal energy is lower than the exergy of electricity,
it is impossible to convert heat to electricity without substantial losses. The amount of heat
that can be converted to electricity depends on what temperature the waste heat has. In
condensing power plants, the steam is cooled by large amounts of water or air to a low
temperature. This way the electricity efficiency is increased, but still about 60% of the input
heat is wasted. In district heating applications, the plant is cooled by the district heating
network, to a temperature around 70-120°C. This means that the waste heat is utilised, but on
the other hand the electricity production is only about 30% of the heat input. This is a trade-
off dictated by thermodynamics –one gets either more electricity and a lot of almost cool
waste heat water that cannot be utilised, or less electricity and waste heat water at a high
enough temperature to be utilisable for example for district heating. However, if the district
heating can utilise lower temperatures, the electricity production of the heat and power plant
can be increased. This was the main motivation of this degree project.
1.2 Methods
The need for heating and hot water varies depending on the weather (determining the heat
losses from the buildings) and the behaviour of the people using the heat and hot water. If
these variations could be predicted, the supply temperature could follow the heat demand. The
delivered heat depends on the temperature of the supply water leaving the heat plant (which is
controlled by the heat plant) and the flow of water through the network (which is controlled
by the consumers). Each consumer will take a certain amount of heat from the water of the
supply line, by sending it through their heat exchangers and exert it to the return line. If the
temperature of the supply water is high, a smaller flow is needed to deliver the requested heat.
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Also, if the heat exchanger can cool the district heating water to a lower return temperature, a
smaller flow is required to deliver the requested heat. When the heat demand is low, it is
therefore possible to have a lower supply temperature, and increase the electricity efficiency
of the CHP plant.
In this project, operational data from the combined heat and power plant Idbäcken was used to
estimate a dynamic model of the district heating network in Nyköping. The repeating daily
variations of the heat load was modelled through differentiation of the signals, and the
weather dependence of the heat load was modelled with an ARX model. A control strategy
using the dynamic model to decrease the supply temperature of the district heating system
was evaluated and compared to the present control strategy of the Idbäcken plant.
1.3 This report
In this report, the methods and results of the project are presented. In Chapter 2, theory on
district heating system dynamics and the relation between supply temperature and electricity
efficiency of a combined heat and power plant connected to a district heating system are
presented. Feed forward control and the basic concepts of empirical modelling are described.
A short summary of related research is also made. In Chapter 3, the combined heat and power
plant Idbäcken in Nyköping and the connected district heating system are described. A
relation between the electricity efficiency and the supply temperature of this plant and the
flow capacity of the network are estimated. Also, some basic features of the load and return
temperature of the system are presented.
One static and one dynamic approach to modelling was used during this project. The resulting
models are presented in Chapter 4. Attempts were made to include not only the outdoor
temperature but also solar irradiation and wind speed as input parameters to simulate the heat
demand. In Chapter 5, a control strategy based on the dynamic model presented in Chapter 4
is evaluated and compared to the present control strategy of the Idbäcken plant. The economic
benefit of the new control strategy is assessed. Finally, in Chapter 6, the results of the project
are discussed, and drawbacks as well as benefits of the new control strategy are suggested
together with ideas of possible improvements of the model.
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2 Theory
In this chapter, the theoretical background for this study is presented. First, the basic concepts
of district heating, the relation between supply temperature and electricity efficiency of a
combined heat and power plant and the dynamics of a district heating network are introduced.
Then the feed forward control method and a bit of theory on empirical modelling are
described. Finally, a summary of recent publications on district heating modelling is made.
2.1 District heating
A district heating (DH) system consists of a heat producer, a transmission network of pipes,
and local substations in which heat from the DH water is transferred to the radiator circuit and
the hot water circuit of the heat consumer. The DH network is called the primary side, and the
consumer circuit - radiator and hot water circuits – are called the secondary side. Every
substation is connected both to the supply (feed) pipe and the return pipe of the DH system, as
shown in Figure 1 (only the primary side is visible in the figure).
Figure 1. Explanatory sketch of the primary side of a district heating network.
A local control system, aiming to meet the momentary heat demand in the house, controls the
flow through the heat exchangers, on both the primary and secondary side. This means that
the flow in the supply and return line is not controlled centrally at the heat plant, but is the
result of the flows through the substations. To work properly, the heat exchangers need a
certain pressure difference between the supply and return line. This pressure difference is
created and maintained by a central pump, usually located at the heat plant. When the flow is
high, the pressure losses throughout the network will increase, and the pump will have to
work harder. The pressure will always be sufficient at substations close to the heat plant, but
if the capacity limit of the pump is reached, the pressure in the distant parts of the grid will
fall, and the heat exchangers situated there will not be able to work properly – these customers
will have cold radiators. This situation must be avoided. Therefore, the temperature of the
supply water is varied with the load variations, so that at times when the heat demand is high,
more energy is transferred with each cubic metre of supply water. In this way, the flow can be
regulated indirectly.
Different DH systems are constructed for different supply temperature levels. The advantage
of a high supply temperature system is that the flow will be smaller, and hence the pipes can
be dimensioned smaller as well. The advantage of a low supply temperature is that the heat
losses from the pipes to the ground will be smaller, and if the heat plant is a CHP plant, the
condensation temperature of the turbine will be lower, ensuring a higher electricity
production. In Sweden, most DH systems are low temperature systems [1].
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2.2 Supply temperature and electricity output
The supply temperature to the district heating network affects the electricity efficiency of the
turbine in a combined heat and power (CHP) plant, since it affects the temperature at which
the steam condenses. The electricity output of a steam turbine depends on the mass flow of
steam through the turbine, the efficiency of the turbine and generator, and the pressure- and
temperature difference of the steam before and after the turbine [2]:
)( 0 ciimP (1)
where
P is the electric power output
m is the mass flow
is the efficiency
0i is the enthalpy per mass unit of the steam before the turbine
ci is the enthalpy per mass unit of the steam after the turbine, in the condenser
Enthalpy is a state parameter used in thermodynamics (see for example [3]) defined as
pvui (2)
where
u is the inner energy per unit mass (which depends on the temperature and the specific
heat capacity)
p is the pressure
v is the volume per unit mass
To increase the electricity generation for a given amount of produced heat, one needs to
increase the enthalpy before the turbine or decrease the enthalpy after it. The temperature
before the turbine is usually limited by the type of fuel used and the durability of the materials
in the combustion chamber and the turbine, and will not be considered in this study. The
temperature after the turbine on the other hand, is limited by the required supply temperature
to and the return temperature from the district heating grid, since the DH water is the heat sink
that cools the steam. The heat transferred from the steam to the DH supply water must have a
sufficiently high temperature to ensure that the DH customers get as much heat as they
consume. If the supply temperature can be decreased, the electricity exchange will increase
[2].
The α-value is a commonly used measure of the electricity efficiency of a heat and power
plant. It is defined as
heat
el
P
P with elheat
th
PPP (3)
where
Pel is the produced electric power
Pheat is the produced heat power
Pth is the supplied thermal power to the plant
η is the plant efficiency
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2.3 Dynamics of district heating networks
The dynamics of a district heating network include processes of very different timescales.
Changes in pressure and flow travel with the speed of sound, and will reach the whole grid in
seconds. Changes in temperature, on the other hand, travel with the flowing water, and will
take hours to be carried out. This will result in loading and unloading effects when the power
output of the heat plant is larger or smaller than the heat consumption on the grid during
different times of the day. In this section the time delays, loading effects and return
temperature dynamics of a district heating system will be described. Also, methods for
calculation and models of the heat load will be presented.
Since the topic for this study is the temperature and flow variations in the system, analysis of
the pressure dynamics is omitted, and a quasi-static view of pressure is used.
2.3.1 Time delays When the output temperature from the power plant is changed, this change will propagate in
the pipes with a speed a bit slower than the speed of the water. The reason for this is that the
walls of the pipe will need to adjust from the former water temperature to the latter, and to do
that they will take heat from the water. The thicker the walls and the narrower the pipe, the
slower the temperature change will travel compared to the water. Also, because of losses to
the ground, the water will be colder when reaching far out on the grid than it was when it left
the plant [1]. However, if these factors are neglected, the transport time of a temperature
change can be calculated according to
t
tt
dQV )( (4)
where
V is the volume of the district heating network
Q( ) is the volume flow emitted from the plant at the time
t is the transport time through the network
2.3.2 Loading/unloading the system Since the transmission on the DH grid is not momentary, and the heat can be delivered at
different temperatures, there is a possibility to load the system with extra energy. If the supply
temperature is increased, the temperature on the grid will increase, and hence the heat power.
If the load is constant, the flow will decrease, since a smaller amount of water need to pass the
heat exchanger to give the same amount of heat. This process is called loading or packing the
network. To avoid high flows the system can be loaded in advance when high loads are
expected, so that the need for an increased flow will be smaller [4].
Tests with step response when increasing the supply temperature show that the loading time
(corresponding to the transport delay of the system) of a DH network is approximately V/Q0,
V being the total volume of supply and return pipes and Q0 being the initial flow from the
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plant. If the load is constant, an increased supply temperature will lead to a decreasing flow.
After the time V/(2Q0), the network is 75 % loaded [1].
2.3.3 Calculation of the heat load A DH system is a large and complex structure. For detailed analyses, models can be built
using software like X-power or pfcsf/pfctf (see section 2.6). There is literature on the subject
of methodically reducing the models of the networks, see for example [5] and [6]. However,
the detailed models are mainly used for analysing the static behaviour of the system,
addressing questions such as which the lowest supply temperature should be. It has been
shown in [1] that for production oriented studies, an extremely simplified model of the
network can be sufficient.
The heat power provided to the district heating network by the heat plant depends on the
supply and return temperature and the flow of the water. These values can be measured, and
the supplied power can be calculated as
))()()(()(sup tTtTtmctP RSp (5)
where
Psup is the power supplied to the district heating system by the heat plant
cp is the specific heat capacity of water
)(tm is the mass flow of the water
TS is the supply temperature at the CHP plant
TR is the return temperature at the CHP plant
However, the power supplied to the district heating network at a specific time is not the same
as the power delivered to the customers (also referred to as the load of the DH network) at
that specific time. This is a result of the transport delays of the system. If the DH network is
approximated as an equally distributed homogenous load, the heat delivered to the load is,
according to [1]:
t
dTdT
tmctP
tt
t
R
t
tt
S
pdel
)()(
)()( (6)
where
Pdel(t) is the delivered power (the load)
t is the transport time one way through the supply or return line
Note that while the expression for the supply temperature is close to reality, since the
temperature from the CHP plant will propagate through the supply line with the flowing
water, the expression for the return temperature is more of an approximation. The return water
from a specific load will be mixed with the water from more distant loads earlier in time, and
more central loads later on. It is not possible to distinguish the return temperature from loads
at a specific time, but the expression above will give a mean value.
Another option is to approximate the DH network with a point load, situated at the load centre
of mass of the system. The load can then be calculated as
12
))2
()2
()(()(t
tTt
tTtmctP RSpdel (7)
With this approximation, the load variations will be exaggerated [1]. However, since the
equally distributed load model to some extent will smoothen out the variations, the point load
approximation may be advantageous for modelling purposes.
2.3.4 Heat load models The heat producer of a district heating system has to follow the heat demand (the load). The
load is time varying and partially stochastic, partially deterministic. It depends on parameters
like the outdoor temperature, the time of the day, coldwater temperature, solar irradiation and
wind speed. The outdoor temperature and the time of the day are most significant. The
coldwater temperature has an impact on the heat needed for hot water preparation, and is
season dependent. A high wind speed increases the heat losses from the walls of buildings,
and thus increases the heat demand, while high solar irradiation contributes to the heating and
decreases the heat demand.
The total load can be seen as a sum of load contributions depending on different parameters:
...wsolTcwdayToutdel PPPPPP (8)
where
PTout is the load contribution depending on the outdoor temperature
Pday is the load contribution depending on the time of the day
PTcw is the load contribution depending on the coldwater temperature
Psol is the load contribution depending on the solar irradiation
Pw is the load contribution depending on the wind speed
The relation between the outdoor temperature and the load PTout can be assumed to be linear
with the boundary condition that PTout is zero if the outdoor temperature is higher than a
certain value. The contribution to the load from daily variations, Pday, has to be estimated
from empirical data. The basic features are that the load is smaller at night than in daytime,
and that there is a peak in the morning and usually in the evening. The morning peak comes
later in the weekends than in the weekdays. This load part depends on what kind of customers
the network supplies.
The load contributions from coldwater temperature, PTcw, from solar irradiation, Psol, and from
wind speed, Pw, can all be assumed to be linear. Since these contributions all are rather small
and to some extent season dependent, they can be modelled by including season dependence
in the model. That way, the transmission losses will also modelled indirectly, since they
depend on the temperature in the ground, which is season dependent [1].
2.3.5 Dynamics of the return temperature Theoretically, heat exchangers give a lower return temperature if the supply temperature is
higher. However, it has been shown in [1] that this relation is not valid for DH systems.
Instead, the return temperature depends on the outdoor temperature and the social load. In
13
cold weather, the return temperature increases with falling outdoor temperature. There is a
break point at an outdoor temperature of approximately 7 C, where the return temperature has
its lowest values. For higher outdoor temperatures, it increases again (see Figure 12 in
Chapter 3). This can be explained by the fact that when it is cold, the heating need dominates
the load. The return temperature from heat exchange to the radiator circuits is higher than the
return temperature from tap water preparation, because the water in the radiator circuit is
never as cold as the cold water supplying the tap water, and therefore cannot cool the DH
water as much. When the outdoor temperature goes up, the tap water preparation becomes a
bigger part of the load, and hence decreases the return temperature of the system. During
really warm days though, the need for heating diminishes and the total load on the system is
small, leading to problems with low flow in the system. To keep the flow up, supply water
might be by-passed to the return line. Also, with low supply temperatures, the heat exchangers
are less efficient. The result is a higher return temperature. Another explanation for why the
return temperature for the whole grid does not follow what heat exchanger theory suggests is
that if some heat exchangers in the system are malfunctioning, giving a high return
temperature, they have a big influence on the return temperature of the whole grid.
2.4 Feed forward control
The supply temperature of a district heating system is typically controlled by feed forward
control (see Figure 2). The idea with feed forward control is to use information of a
measurable disturbance on the system (the outdoor temperature) to compensate for its effects
(the load variation). This means that some model of the relation between the load and the
outdoor temperature is used to calculate the control point of the supply temperature. The
reason to use feed forward control is the long transport delays in the system. If instead the
load would be calculated and feed-backed to the supply temperature calculation, the response
would be hours too late. The difficulty with feed forward control is to make a good model of
the relation between the disturbance signal and the output of the system. Usually, a control
curve where the supply temperature increases linearly with decreasing outdoor temperature
under a certain break point is used. The break point corresponds to the lowest supply
temperature that will ensure the statutory hot water temperature [7].
Figure 2. Feed forward control. Here, v is the measurable disturbance signal, F is the regulator, u is the
input signal, G1 and G2 is the system that should be controlled, H is the transfer function of the
disturbance and y is the output.
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2.5 Empirical modelling
To use feed forward control of the supply temperature, a model for calculation of the supply
temperature from some input parameters is needed. Usually, simple static models like control
curves are used. In this project, a more complex static model and dynamic models estimated
from empirical data were used instead.
Empirical modelling, also called system identification or black box modelling, means building
mathematical models using data collected from the modelled system, rather than the physical
relations of the system (which are used in physical modelling). The advantage of empirical
modelling is that complex systems can be modelled without knowledge of the details of the
system. Only the relevant input and output signals of the system needs to be known to
estimate a black box model.
A dynamic model uses not only the current input signal but also earlier input and output
signals to calculate the current output. This means that dynamic behaviour can be described.
For example, the temperature inside a house will not drop immediately if the outdoor
temperature drops, but will depend both on the outdoor temperature now and the outdoor
temperature the last hours, since heat is stored in the house structure. Also, if the heat on the
radiators is increased, the indoor temperature will rise slowly. A static model will only be able
to describe the temperature indoors if the outdoor temperature and the heat on the radiators
are constant for some time, so that the system stabilizes.
A general linear dynamic black box model can be written
)()(
)()(
)(
)()( te
qD
qCtu
qF
qBty (9)
where
y(t) is the output signal
u(t) is the input signal
e(t) is white noise
B(q), F(q), C(q) and D(q) are polynomials of the shift operator q
The B(q) and F(q) polynomials model the input signal’s effect on the output signal, and the
polynomials C(q) and D(q) models the noise of the system. The shift operator q is equivalent
with the z-transform, and shifts a time series back or forward in time. It is used to describe
that the output at a specific time depends not only on the output and noise at that time but on
previous values of output, input and noise.
The model (9) is called the Box-Jenkins (BJ) model. In many cases, a simplified version of
the BJ model, where one or more of the polynomials are set to be ≡1, can be used. If
C(q)/D(q) ≡1, the model is called the Output-Error-model, because the noise e(t) will be the
difference between the real output and the undisturbed output. If the polynomials
F(q)=D(q)=A(q), the model is called the ARMAX model (Auto Regression Moving Average
eXogen variable). In the ARMAX model, the input and the noise are subjected to the same
dynamics. This should be the case if the noise enters the system early. An ARMAX model
with C(q) ≡1 is called an ARX model. In Figure 3, the structure of the ARX model is
15
displayed. An ARX model with A(q) ≡1 is called a FIR (finite impulse response) model. A
FIR model calculates the output from old inputs only [8].
Figure 3. Block diagram of the ARX model.
2.5.1 The ARX model In this study, the ARX model was used and will therefore be described in more detail. The
equation for the ARX model is
)()()()(
1)(
)(
)()( tvtwte
qAtu
qA
qBty (10)
If the structure parameters of the model, describing the number of parameters ai and bi in the
polynomials A(q) and B(q) are denoted na and nb, the undisturbed output w(t) is
)(...)1()(...)1()( 11 natwatwanbtubtubtw nanb (11)
and the disturbance term v(t) is
)()(...)1()( 1 tenatvatvatv na (12)
The output y(t) can then be written
)()(...)1()(...)1(
)())()((...
))1()1(()(...)1()1()()()(
11
11
tenatyatyanbtubtub
tenatvnatwa
tvtwanbtubtutbtvtwty
nanb
na
nb
(13)
The parameters a1, a2, ..., ana and b1, ..., bnb can be chosen so that the model fits the data y(t) as
well as possible in a least square sense. This is called model calibration, and can be done with
the Matlab System Identification toolbox. The model order, that is the value of the structure
parameters na and nb, should be chosen with care. If there are too few parameters, the model
will not be able to describe the system dynamic properly. If there are too many parameters,
the model will be over fitted, and follow not only the dynamic of the system but also the
specific noise of the calibration data series. To avoid over fitting, cross validation can be used.
This means that one data set is used to calibrate the model, and another data set is used to
validate the model. The number of parameters should only be increased if it improves the fit
to the validation data [8].
16
2.5.2 Prediction with the ARX model Once the model is calibrated and validated, it can be used for simulation or prediction of the
system. In simulation, the model is presented with new input data, and calculates the output
from these input data and the modelled output data. In prediction, the model is presented with
both new input data and delayed output data. Predictions of the output are made from the last
known real output, old predictions of outputs and new inputs. The time difference between the
last known real output and the predicted output is called the prediction horizon.
To make a prediction with the prediction horizon k, a k-step predictor is needed. The model is
then written in state-space form. The state x(t) of the system is defined as
)(
...
)1(
)(
)1(
...
)1(
)(
nbtu
tu
naty
naty
ty
tx (14)
Written in matrix form the new state x(t+1) will be
)(
0
...
...
...
...
...
...
0
1
)(
0
...
0
1
...
...
...
...
0
)(
01...000......0
...........................
.........1...............
0......000......0
0......001......0
...........................
.....................10
0......00......01
......
)1(
11121
tetutx
bbbaaaa
tx
nbnbnana
(15)
The system can be described by
)()()(
)()()()1(
tetHxty
tKetGutFxtx (16)
where
]......[ 11 nbna bbaaH (17)
The prediction error ε(t) is
17
)(ˆ)()( txHtyt (18)
The optimal predictor for this case, see for example [9], is given by
)()()(ˆ)1(ˆ tKtGutxFtx (19)
Denote KHF . Then the predicted state after two time steps will be
)()1()()(ˆ)1()())()(ˆ(
)1())()()(ˆ(0)1()1(ˆ)2(ˆ
tFKytGutFGutxFtGutFGutKytxF
tGutKytGutxFtGutxFtx (20)
The predicted state after three time steps will be
)()2()1()()(ˆ0)2()2(ˆ)3(ˆ 222 tKyFtGutFGutGuFtxFtGutxFtx (21)
The general k-step predictor can then be written
)(ˆ)(ˆ
)()(ˆ()()1()(ˆ)(ˆ 111
0
1
ktxHkty
tKykxFtKyFpktGuFkxFktx kkk
p
pk
(22)
If the prediction horizon is varying, predictions over different horizons can be done
simultaneously using the following matrix expression.
)(...
)1(
...
)1(
)(
......
............
...0
0...0
)(ˆ...
)(ˆ
...
...
)1(ˆ
ˆ
101
0
0
1
ty
KHF
HFK
HK
Ntu
tu
tu
GHFGHF
GHFHFG
GHF
tx
HF
HF
H
Nty
ty
Y
NNN
t (23)
With this predictor, measured output signals up until time t and input signals up until time t+k
are used to predict the output y(t+k), for 1<k<N. When modelling the heat load of a district
heating system, more recent values of the input signals than the output signal are known, since
the calculation of the load is delayed by the transport of the return water from the load to the
heat plant where it is measured.
If the modelled system has more than one input signal, the same predictor can be used, but
with u(t), nb and b1, ..., bn as vectors.
During the calibration and validation process, among other things the fit of the models were
compared. Fit is used in the Matlab System Identification Toolbox as a measure of the percent
of the measured output y that is explained by the model, and is defined as
))(
ˆ1(*100
ymeany
yyfit (24)
where
18
y is the output predicted by the model
y is the real output.
2.5.3 Time dependent variations The black box models described in 2.5.1-2.5.2 model the output of a system from an input
signal that is correlated to the output. One part of the heat load is linear function of the
outdoor temperature, and should be possible to describe by such a model. However, the heat
load also has a component that depends on the time of the day and the day of the week, the
social load. This part of the load is not correlated to any input signal to the system, and should
therefore be modelled in another way.
Since the social load is following a certain repeating pattern, one method is to assume that it is
the same as the day before. The input and output signals of the system can then be
differentiated with respect to a 24 hour interval, applying the 24 hour differential operator Δ24
that calculates the difference between the value now and the same time yesterday to the input
and output signals, as shown in (25). To model the difference between weekdays and
weekends, the week differential operator Δ168 can be used. This operator computes the
difference between the value now and the value the same time one week ago. If both the day
and week differential operator is used, one compares the difference of the difference between
now and yesterday, and between one week ago and the day before that [10].
1921682416824
16824
168
168
24
24
1)1)(1(
)1(
)1(
qqqqq
q
q
(25)
The model applies the operator Δ24 Δ168 to the input parameters, and then predicts the load
difference y’, from which the load y can be computed:
19216824
19216824
)()()()(')(
)1)(()('
qtyqtyqtytyty
qqqtyty (26)
An advantage with this method is that it also takes care of the season dependence of the
model. Parameters such as cold water temperature and temperature in the ground, as well as
the seasonal variations of solar irradiation and wind speed will not change much from one
week to another, and will therefore be sufficiently modelled by the reversed differentiation,
and will not interfere with the parametric model.
2.6 Previous research
In the beginning of this degree project, a literature study was carried out to find out about
available modelling tools and methods for district heating networks. Of special interest was
the use of dynamic models to simulate and control the supply temperature of a district heating
system. It was found that many different methods are used to model district heating networks,
but generally the models are static or quasi-static. Some authors claim that modelling the
dynamics is unnecessary; others simply find it outside the scope of their studies.
19
For modelling of district heating systems, many different methods are described in the
literature. There is dedicated software such as X-power and pfcsf/pfctf, which can handle
detailed network models as well as simplified models. In many cases, a simple model is
enough. What kind of model that is needed depends on what focus the analysis has. Larsen,
Bøhm and Wigbels compares a Danish and a German method of aggregating networks in [5],
which both work well on their test case. With these methods, the number of pipes in their
model could be reduced from 44 to 3 or 10 respectively, without increasing the error in return
temperature and heat production calculations. The Danish method is compared to the network
model software TERMIS in [11]. With both methods, the dynamics at a district heating
consumer could be modelled fairly well using data from the heat plant, unless the consumer
was located at distant pipelines with many bends and fittings. In [6], yet another network
aggregation method is presented, based on simulations with pfcsf/pfctf. At Vattenfall in
Uppsala, a detailed network model is simulated with the software X-power [12]. However, the
detailed models and aggregation methods are necessary mainly for analyses of the network
itself, to answer questions about the heat distribution and pressure levels in the different parts
of the grid and what the bottlenecks of the system are. For production analyses, it can be
enough to use a gross approximation of the network. In [1], Larsson compares simulations of
a detailed network model with approximations of the network as a point load and as an
equally distributed load. The results from the different models are quite similar.
Attempts to combine a production model with a distribution model are made by for example
[6], [13] and [15]. Kvarnström, Dotzauer and Dahlquist models both production and
distribution with Mixed Integer Programming (MIP), and shows in [6] that the production
costs of the district heating system in Stockholm would be lower if the production model used
to determine which production unit to use was extended with a distribution model. In their
distribution model, the transport delay on the grid and the return temperature are
approximated to be constant. What kind of load model they use is not explicit in the report.
Keppo and Athila present a similar study in [13]. They also use MIP to model the heat
production, and combine it with a district heating network model. The distribution model
models supply and return temperatures at the secondary side of the substations as linear
functions of the outdoor temperature. The temperatures and flow on the primary side are
calculated according to heat exchanger theory. The transport delay on the network is omitted.
In both [6] and [13], the heat demand of the consumers is assumed to be a function of only the
outdoor temperature. This means that the load variation due to the daily behaviour of the
consumers, the social load, is neglected. Larsson describes a strategy to include these load
variations in the distribution model in [1]. The heat load is modelled as a sum of a linear
function of the outdoor temperature and a higher order function of the time of the day. These
functions are also adjusted to the season. Larsson implements this load model with the
software pfcsf/pfctf, with which the transport delay of the system can also be modelled.
Larsson’s model is verified on the district heating network in Karlskoga in [14]. The aim in
that case was to reduce the flow variations to avoid reaching the distribution limits of the
network. This was successful – the maximal flow was reduced with 7% and the minimal flow
was increased with 12%. The same modelling method is also used by Johnson and Rossling in
[15] and by Hedin in a degree project at Vattenfall in Uppsala [16]. A similar model approach
is used in [17]. The outdoor temperature dependent part of the load is in that study modelled
with piecewise linear polynomials, and the social load is modelled with one constant value for
each hour of the week. This model is compared with the ARMA model used by the software
Aiolos, and it is found that the models give approximately the same result, since the more
sophisticated ARMA model suffers more from errors in the temperature prognosis. In [18],
20
sine and cosine terms are used to model the social load and a binary variable is used to
distinguish between weekdays and weekends.
In [19], a time series analysis of outdoor temperature prognoses and heat load variations on a
district heating system is compared to using neural networks. Malmström et al show that the
temperature prognoses provided by for example SMHI could be improved by time series
analyses using data from the heat plant site. Three heat load models are compared: a
SARIMAX model (a dynamic model that uses differential operators), an ARX model using
both recent values of the input and output signals and values from around 24 hours earlier,
and a neural EBP network model, and the conclusion is that time series analysis models are
better suited to predict district heating loads than at least this type of neural network model.
The SARIMAX model structure is also used with good results for prediction of electricity
consumption in [20].
Research on increasing the electricity efficiency of a CHP plant is abundant. Decreasing the
supply temperature is suggested by for example Jansson in [21] and Axby et al in [22]. It is
stated by Axby et al that a lower supply temperature affects the electricity production more
than a lower return temperature. In their study, the potential gain from a 5°C lower supply
temperature is 4.2 GWh/year for the 170 MW CHP plant in Örebro and 6.2 GWH/year for the
155MW CHP + 300MW heat plant in Västerås. Decreasing the return temperature with 5°C
would only give 1.1 or 1.7 GWh/year respectively.
21
3 Case study
In this chapter, the combined heat and power plant Idbäcken and the district heating network
of Nyköping are described. A relation between supply temperature and electricity output is
derived, and the flow limit of the district heating network is examined.
3.1 Idbäcken’s CHP-plant
The main production of the district heating plant Idbäcken of Nyköping, which is shown in
Figure 4, is handled by the 105 MW boiler (P3), that provides the combined heat and power
(CHP) part of the plant with steam. One high-pressure (HT) and one low-pressure (LT)
turbine together produce 35 MW electricity, and from the exhaust steam, 58 MW heat is
transferred to the district heating system by two condensers. A flue gas condenser (Rgk) of 12
MW is used to preheat the return water. When the demand for heat is higher, two heat boilers
(P1 and P2) of each 35 MW can be used. There is also an electric boiler (EÅP) of 14 MW and
two substations, Lasarettet (LAS) and Brandstationen (BRA), of totally 75 MW connected to
the supply line of the district heating system, and a gas boiler (Gaspanna) of 1 MW connected
to the return line. There is a hot water accumulator tank that can hold 400 MWh heat, and also
an external cooler (not visible in Figure 4) called “Beriden” which is connected to the return
line. When the electricity price is high but the heat demand of the district heating customers is
modest, “Beriden” is used to cool away heat from the district heating network. Then the
production can be increased, and more electricity can be sold. Typically, “Beriden” is turned
on and off irregularly on a daily basis. If the heat demand is low, the first step is to reduce the
heat extracted from the flue gas condenser. The second step is to start “Beriden”. The third
step is to reduce the combustion of the boiler.
Figure 4. Explanatory sketch of the CHP plant Idbäcken.
22
The bottom line of the heat production of Idbäcken is determined by the heat load applied by
the district heating system. To meet the load, a sufficient supply temperature must be
delivered from the plant. The control point for the supply temperature is derived from the
control curve in Figure 5. This control curve was originally linear between the upper and
lower saturation temperatures and had its lower break point at the outdoor temperature 10 C,
but it has been adjusted from time to time according to experience.
Figure 5. Control curve for the supply temperature of the Idbäcken CHP plant.
3.2 The district heating network of Nyköping
A map of the district heating network of Nyköping can be seen in Figure 6. The heat plant is
situated in the left down part of the middle cluster. The pipe system contains of 130 km pipe
with a volume of 8000m3, of which half is the supply line and half is the return line. The total
water volume of the system is about 18 000m3, since there is also an accumulator tank for
heat storage at the heat plant in Idbäcken which is connected to the network. At the 450
biggest sub stations, measurements of flow, differential pressure, supply temperature and
return temperature are made.
23
Figure 6. Map of the district heating network in Nyköping. The green lines are the district heating pipes.
3.3 Electricity output and supply/return temperature
To determine the relation between the -value (the produced electricity divided by the
produced heat, see also section 2.2) and the supply and return temperatures respectively, two
different approaches were used. First, an experiment was carried out at the plant, where step-
wise changes were made in the supply and return temperatures respectively, while other
parameters were kept as constant as possible. Secondly, the result from the experiment was
verified by analysis of operational data from other time periods with higher temperature
levels.
In the step experiment, the electricity production was kept constant while the supply and
return temperatures were varied with 5 C each, leading to a change in heat production as well.
The -values for the four different states were calculated. The -value is assumed to be
negatively proportional to the supply and return temperatures, if all other parameters are
constant:
24
RRR
SSS
TkT
TkT
)(
)( (27)
Where
Δα is the change of the α-value due to a change in supply or return
temperature
kS, kR are proportionality constants
ΔTS, ΔTR are changes in the supply and return temperatures
An estimation of the proportionality constants kS for change of the supply temperature and kR
for change of the return temperature can then be made from the measured values. The
measured values of the parameters can be seen in Table 1.
Table 1. Result from the -value experiment.
Supply temperature [°C] Return temperature [°C] Alpha value 74.2 46.9 0.579 74.4 49.9 0.574 79.5 50.7 0.565 79.6 45.1 0.571
This experiment gave the values
0015.0
0017.0
R
S
k
k
Since the measured data points in the experiment described above were few and not very well
spread, there was a need to validate the result with operational data. However, to find
sequences of operational data where the return temperature is constant while the supply
temperature changes is difficult. Generally, the supply temperature is stationary, but the return
temperature is subject to frequent variations. Hence another approach than the one above is
needed to validate the values of the constants.
The share of produced electricity compared to heat, the -value, depends on the condensation
temperature of the steam, as described in chapter 2. Steam leaves the turbine at two different
pressure levels, and is cooled by two different heat exchangers (see Figure 7). The district
heating return water first cools the low pressure steam and then the steam with a bit higher
pressure, leaving the last heat exchanger with the temperature required for the DH supply line.
Depending on the load, different amounts of steam goes to each heat exchanger. This means
that some of the steam condensates at a temperature close to the supply temperature, and
some condensates at a temperature close to the return temperature. The impact of each of
these two temperatures compared to the other depends on the load.
25
Figure 7. Heat balance for the CHP plant Idbäcken. The steam leaves the low pressure turbine LP160H at
two stages and the heat is transferred to the district heating network (coming in from the right) in two
heat exchangers, before the steam ends up in the condenser.
To simplify, it was assumed that the mean condensation temperature at any given time is the
mean value of the supply and return temperatures. Then data from the operation of the power
plant was used to find a linear relation between the -value and the condensation temperature.
Data from reasonably stable operation at 40-50 MWth during the years 2005/2006 and
2006/2007 was chosen [23]. Mean values of the supply and return temperature and the -
value were calculated for the selected time periods, and a linear relation was estimated using
the Matlab function polyfit, which is based on the least square method (see Figure 8).
26
50 55 60 65 70 75 800.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
Condensation temperature, centigrades
Alp
ha v
alu
eEstimation of the relation between alpha value and condensation temperature
Operation data 2006/2007
Operation data 2005/2006
Experiment data October 2007
Linear regression
Figure 8. Estimation of the relation between the alpha value and the condensation temperature.
The slope of this linear regression is -0.0041, which is about twice the slope calculated from
the experiment described above (kS and kR). This is reasonable, since a change in either supply
or return temperature will give a change of the condensation temperature that is about half as
big.
As can be seen in Figure 8, the data points are spread, and seem to differ between different
years. There are a number of reasons for why this relation is difficult to detect from process
data. Except for the condensation temperature, the parameters before the turbine affects the α-
value, and the division of the steam to the two condensers differ depending on the heat load.
Sometimes, steam is also drawn off to other applications, for example warm keeping of the
other boilers or the combustion oil. In the following, it will be assumed that the constant kS =
0.0017 calculated from the step experiment is valid for any change of the supply temperature.
3.4 Maximal flow on the DH network
The flow on the DH network is determined by the flow through the substations. Each
substation has to transfer enough heat from the supply water of the DH grid to the secondary
system in the house(s) connected to the substation, to ensure that the heat and hot water
demand is met. The flow will therefore depend on the heat demand and the temperature of the
supply water. With the goal of keeping the supply temperature as low as possible, it is
necessary to determine the upper limit for the flow (which depends on infrastructure such as
pipes, pumps etc).
In Figure 9, the situation when the supply temperature is too low compared to the heat
demand is illustrated. A shortage of delivered heat will manifest as a low pressure difference
between the supply and return line in the substations in the weakest part of the grid, furthest
away from the power plant. That is because the substations closer to the power plant are
taking a big amount of water from the supply line. The central pump of the network,
27
controlled by a certain pressure difference in such a weak point on the grid, will then work
harder, so that the pressure on the grid increases. A higher flow on the grid leads to greater
pressure losses in the system, and a higher pressure from the heat plant is therefore needed. If
the flow increases too much, the pump will not be able to keep up the pressure enough. The
pressure difference in the periphery of the grid will fall, and the heat exchangers will not be
able to transfer enough heat to the secondary systems. People will complain about cold
radiators.
Figure 9. Heat deficit on the district heating network, illustrated by operational data 2006-10-24 22:50 to
2006-10-25 15:30 [23]. Mass flow, pump frequency and pressure difference are normalised to enable visual
comparison.
To determine the flow limit for the model of the district heating network, the pump frequency
is plotted against the flow of the district heating water, see Figure 10. From this plot one can
deduce that a linear trend can fairly well describe the relation between the flow and the pump
frequency. It also indicates that the flow preferably should be kept under 2000 t/h, and
definitely below 2100 t/h. In Figure 9, the pump frequency hits the roof at the flow 2000 t/h.
However, depending on how fast the flow is changing, the flow that the pump can sustain will
differ, so the flow limits are not absolute, which can also be seen from the divergence of the
data points in Figure 10.
28
Figure 10. Pump frequency as a function of mass flow, operational data 2006/2007 [23].
3.5 Load and return temperature characteristics
To get a general understanding of the system, it might be interesting to have a look at the
operational data to see how the load and return temperature depends on the outdoor
temperature in the Nyköping case.
In Figure 11, the calculated load is plotted against the outdoor temperature. One can see that
the load is decreasing linearly with increasing temperature, with a break point at around 15°C,
over which the load seems constant in relation to the outdoor temperature. One can also see
that there is great variation in the data, for example is the load at 0°C spread from 30 MW to
70 MW. Some of this variation depends on the repeating pattern of the social load, and some
of it is of a stochastic nature.
29
Figure 11. Outdoor temperature dependence of the load, calculated from operational data February to
May 2007.
A similar plot of the return temperature is shown in Figure 12. In cold weather, the return
temperature is decreasing with increasing outdoor temperature. However, for outdoor
temperatures above 10°C, the return temperature is instead increasing. This is also the
expected behaviour according to the line of argument in Chapter 2. Data from year 2003/2004
is chosen in this plot because in later years, the return temperature is manipulated with the
external cooling device, which means that the unaffected return temperature from the load is
unknown.
Figure 12. Outdoor temperature dependence of the return temperature, operational data September to
May 2003/2004.
30
4 Modelling of the heat load
In this chapter, the models developed in this project are presented. First, a static model based
on the method described in [1] was tried. Then, a dynamic model based on the empirical
modelling methods described in Chapter 2.6 was developed. The static model is described
more briefly in this report, since the dynamic model was able to describe the system more
accurately, and therefore was developed further than the static model.
The data used for calibration and validation of the load model was supply temperature, return
temperature, mass flow and volume flow out from the CHP-plant Idbäcken in Nyköping to the
district heating network, the outdoor temperature measured at Idbäcken and the cooling power
of “Beriden”, a cooling device which lowers the temperature of the return water. The
sampling time was 10 minutes. Data points that were suspected to deviate due to operational
disturbance were replaced [23].
4.1 A static model
For the static heat load model, data from August 2006 to May 2007 was used for calibration
and data from September to December 2007 was used for validation. The heat load was
modelled as a sum of an outdoor temperature dependent parameter, a time and weekday
dependent parameter and a season dependent parameter (see Figure 13).
)__(),()( yearofdayPweekdaytimePTPP SdayoutTheat (28)
Figure 13. Explanatory sketch of the static load model
The outdoor temperature dependent parameter PT was assumed to be a linear function of the
outdoor temperature Tout, with a break point at the temperature 15°C, above which PT is
constant. PT was determined through linear regression on the calibration data set, and can be
seen in Figure 14.
37.0467.2)( outoutT TTP (29)
31
Figure 14. The outdoor temperature dependent part of the heat load, PT(Tout) , was estimated as a linear
function of the outdoor temperature. The offset level was removed so that the PT-function was zero for
outdoor temperatures over 15°C.
When PT had been determined, the season dependence was analysed. The part of the load
depending on the outdoor temperature was subtracted from the load, and then a floating mean
value over a month (20 days for weekdays and 8 days for weekends) was calculated. This
mean value can be seen in Figure 15. The seasonal dependent parameter PS is the value stated
by this diagram.
Figure 15. Season curve of the heat load, PS(t).
Finally, the time-of-day dependence for weekdays and weekends was analysed. The time and
weekday dependent parameter Pday was approximated as a 10th
order polynomial fitted to the
32
load data reduced from the impact of the outdoor temperature variations and the seasonal
variations by subtracting PT and PS. The data was divided into sets based on day and month,
for example weekdays in December or weekends in April. For each month, one polynomial
for the daily load variations on weekdays and one polynomial for the daily variations of
weekends were determined using the Matlab function polyfit, which is based on the least
square method. In Figure 16 the polynomial for weekdays in March is presented as an
example. Generally, the curve for the winter months have a larger peak without the dip at
midday, and the autumn and spring months are flatter but with more exaggerated morning and
evening peaks.
Figure 16. Example of a daily load curve, Pday(t).
This method was inspired by the method used by Larsson in [1], but is not exactly the same.
Larsson uses the parameters PT and Pday, and makes both of them season dependent, that is he
makes these polynomials differ from month to month. In this project, only one PT function
was used for the whole year, and the PS function was included to model the offset level that
would otherwise end up in the Pday-functions.
When simulating the heat load with the static model, the seasonal and daily variations are
summed up to a combined data series, and then the value of PT(Tout) is calculated and added to
the appropriate value from that data series. Obviously, it is important to fit the simulated year
to the data series in such a way that the weekends correlate with each other. In Figure 17 and
Figure 18, the result from simulating the model with the validation data series is presented. In
the first figure, some days with medium load are shown, and in the second figure the load is
higher.
33
Figure 17. Simulation of the load with the static load model, medium load case.
Figure 18. Simulation of load with the static load model, high load case.
The model is performing fairly well, but is not able to follow all the variations of the real
load. An obvious drawback with this kind of model is that it is sensitive to changes in the
offset level of the heat load. Also, to use only one year to calibrate the model means that there
probably is a substantial noise level in the model, for example in the load mean value curve.
To improve this model, several years should be used in the calibration.
4.2 Dynamic model
For the dynamic heat load model, data from 1st of August 2003 to 31
st of May 2004 was used
for calibration and data from the 1st of February 2007 to the 31
st of May 2007 and 1
st of
34
September 2007 to 7th
of January 2008 was used for validation. The heat load model is
combined with functions for calculation of recent transport delays, estimation of future
transport delays and calculation of recent loads.
The input signals to the overall model are district heating supply temperature, return
temperature, mass flow and cooling power of “Beriden” used to calculate previous loads,
volume flow used to calculate and estimate transport delays on the grid and outdoor
temperature [23], solar irradiation [24] and wind speed [25] used to predict the load on the
grid with an ARX model. The output of the model is a control point for the supply
temperature.
Figure 19. Block diagram of the model structure. Q is the volume flow of DH water out of from Idbäcken,
m-dot is the corresponding mass flow, TS is the measured supply temperature, TR is the measured return
temperature, Tout is the outdoor temperature and P-hat is the predicted heat load.
In Figure 19, the structure of the dynamic model is displayed. First, the recent transport delay
on the district heating network is calculated and an estimation of the future transport delay is
made. Then, the previous load is calculated. The value of the previous load is used to predict
the future load, together with the outdoor temperature. Each of these steps is described in
more detail below.
4.2.1 Calculation of previous load In the model, the previous load on the DH network is calculated for each time step. The
information from this calculation is used to make a prediction of the future loads. The
previous load is
))()()(()()( , tTktTltmcltPtP RSpdelheatheat (30)
where
Pheat(t) is the heat load calculated at time t, corresponding to the heat delivered to an
imagined point load at time t-l
l is the transport time one way from the plant to the point load or vice versa
cp is the specific heat capacity of water
35
m is the mass flow of district heating water
TS is the supply water temperature
TR is the return water temperature
k is the prediction horizon (time of a return travel from load to heat plant to load)
4.2.2 Time delays and prediction horizon Basically, there are two interesting time parameters in the model – the time of a one-way
travel of the water between the CHP plant and the load and the time of a return travel between
the two. The one-way travel time was denoted l and the return travel time was denoted k.
For each time step, the transport time k is calculated as
VdQ
t
kt
)( (31)
where
Q is the volume flow on the network
V is the volume of the district heating network, i.e. 8000 m3
This means that when a volume of water as big as the network volume has been pumped out
of the plant, it is assumed that the water has travelled to the imagined point load and back. In
the same way, the one way transport time l is calculated as
2)(
VdQ
t
lt
(32)
Also, the future values )(ˆ ltl and )(ˆ ltk are predicted. The value )(ˆ ltk is used as
prediction horizon for the load estimation and is calculated as )(ˆ)()(ˆ ltltlltk . The
value of )(ˆ ltl is estimated from the mean value of the last samples of the flow (the future
flow is here estimated to be the same as the present flow).
4.2.3 Load model The load model predicts the load on the DH network using the 24 hour difference of the input
and output signals and prediction with an ARX model. The input signal to the load model was
the measured outdoor temperature. To assess the possible improvement of the load predictions
if an outdoor temperature prognosis was available, real future values of the outdoor
temperature was used as “prognosis” in some simulations. The output signal of the load model
was the heat load on the district heating system. It was also tried to use wind speed and global
solar irradiation as input signals together with the outdoor temperature (global solar
irradiation means that both direct and diffuse irradiation is included). The data on wind speed
was obtained from measurements made at Skavsta, the Airport of Nyköping, by SMHI [25].
The solar data was obtained from STRÅNG [24].
36
4.2.3.1 Differentiation of input and output signals
To model the time dependent social load, differentiation of the input and output signals were
used (see also section 2.5.3). Using the 144 -operator (that is 24 hour differential operator Δ24
converted to the sample time 10 minutes), the differentiated input signal )(tTout became
)144()()( tTtTtT outoutout (33)
When differentiating the output however, one must take into account that there is a varying
transport time in the system. The load calculated at time t was actually applied to the system
at time t-l, where l is the transport time of the return water from the imagined point load to the
plant. Since l is varying, the load must be differentiated with )144()(144 tltl -operator:
))144()(144()()( tltltPtPtP heatheatheat (34)
Then, the reversed differentiation is:
))144ˆ()ˆ(144ˆ()ˆ(ˆ)ˆ(ˆ ktlktlktPktPktP heatheatheat (35)
During the modelling process, it became evident that even though there is a repeating pattern
from one day to another, there is also a considerable variation that is not due to either outdoor
temperature variation or is repeating daily or weekly. To dampen out the noise from
yesterday’s load, which is added in the reversed differentiation, it was tried to differentiate the
signal with a mean value of the values from the last days instead of only yesterday’s value.
This turned out well. The number of days used to calculate the mean value was varied, and
four days were chosen since it gave good result without making the model unnecessary
complex. In Figure 20, the fit of a third order ARX model with different number of days used
in the differentiation is shown.
Figure 20. Comparison between the fit of a third order ARX model depending on how many days the
mean value used for differentiation depends on. 50-step prediction is used.
37
The differentiation used in the model (using the mean value of four days) is thus
4
))576()(576())432()(432())288()(288())144()(144()(
tltltPtltltPtltltPtltltPtPP heatheatheatheat
heatheat
(36)
The social load on a DH network is known to vary not only with the hour of the day, but with
the day of the week, especially depending on if it is a weekday or weekend. This week based
variation could also be seen in the data from Idbäcken. However, attempts to model this
variation by differentiation of the signals with respect to week did not improve the result
compared to using only the daily differentiation. Therefore, the weekly variations were not
included in the model.
4.2.3.2 Choice of model structure, calibration and validation
The weather dependence of the heat load was modelled by a black box model. The model was
calibrated with data from August 1st 2003 to May 31
st 2004. This year was chosen since it was
the last year before the cooling device “Beriden” was taken into operation. That way, the
disturbance from the turning on and off of the cooling device could be avoided in the
calibration. Also, data from the operation of “Beriden” before February 2007 was missing in
the database, and hence the time period with complete data was judged insufficient for both
calibration and validation. To assess the appropriate structure, order and time delay of the
model, various models were estimated and compared. The use of wind speed and solar
irradiation as additional input parameters was also tried. A comparison of some of the models
is made in Figure 21, Figure 22 and Figure 23. In these plots, the fit of the models to the
differentiated data is presented. This fit is lower than the fit to un-differentiated data of the
model including the differentiation and reversed differentiation in Figure 20.
Figure 21. Calibration of the ARX load model with differentiated data and 50-step prediction. The models
are described with “order of A-polynomial”/”order of B-polynomial”/”delay” in the figure. Some
ARMAX models and the best ARX models using also wind speed and solar irradiation (WS) as input
parameters are presented as well. 50-step prediction is used.
38
Figure 22. Validation of ARX load model, with data from February to May 2007 and 50-step prediction.
Figure 23. Validation of ARX load model with data from September to December 2007 and 50-step
prediction.
The choice of model structure was made early in the process. The ARX-structure was chosen
because it is the simplest model structure that models the prediction error. Since it is possible
to currently calculate previous loads of the system, the prediction error can be calculated and
used in the following predictions. An Output Error model would not be able to use this
information. The more complex ARMAX and BJ model structures were considered, but since
they did not considerably improve the performance of the model, the simpler ARX structure
was judged sufficient.
When wind speed and solar irradiation was used as input signals, they were first weighted
with the current outdoor temperature, because both wind speed and solar irradiation should
have a bigger impact on the heat demand in cold weather than in warm weather. This was
done by multiplying the signals with 15-Tout, and the outdoor temperature Tout was set to be
39
maximally 15°C. As can be seen in Figure 11, the load has a break point and does not
decrease with outdoor temperatures higher than 15°C, and then sun and wind should not
affect the load either.
In the end, the ARX model with third order A- and B-polynomials was chosen, since the
validation showed that higher orders did not considerably improve the performance of the
model. The model was
321
31
02957.002101.096.01
)()()4352.003065.05358.0()(
qqq
tetuqqty (37)
4.2.4 Result of the dynamic modelling The four parts of the dynamic model – the calculation of the transport delay, the estimation of
the prediction horizon, the calculation of previous loads and the load predictor – were
combined within a Simulink model structure. The model was run with data from the
validation periods. The prediction horizon varied with the flow, and were generally between 4
and 12 hours.
The model output was compared to the calculated (“real”) load for two example periods,
presented in Figure 24 and Figure 25. The first is a case when the load is high (around 75
MW), and the second is a case when the load is medium high (around 55 MW). The second
case is also an example of the model’s reaction to anomalies, since it contains the Easter
weekend of 2007.
In Figure 24, the modelled load is compared to the calculated load for few days in February
2007, the high heat load case. One can see that the load model follows the real load fairly
well, but underestimates the load at the extra high morning peak the 21st of February, and
overestimates the load at some of its dips.
40
Figure 24. K-step prediction of the load with the dynamic model, high load case, Februrary 2007.
For the medium load Easter case in Figure 25, the model cannot follow the real load as well as
in the high load case. The main mistake takes place in the morning the 7th
of April, which is
Easter Saturday.
Figure 25. K-step prediction of the load with the dynamic model, medium load case, April 2007.
41
4.3 Comparison of the static and dynamic model
To be able to compare the static and the dynamic model, the fit of the respective models to the
data of the period 1st of February to 20
th of May 2007 were calculated. The static model was
simulated and the dynamic model was run with 50-step prediction. The fit of the static model
was 37% and the fit of the dynamic model was 70%. When the dynamic model was run in the
Simulink model structure with variable and uncertain transport delay and prediction horizon
and with the effects of the external cooling device “Beriden” included, the fit was only 48%.
This is a substantial loss in performance, but still better than the static model, which would
also need to deal with the flow variations if it was used instead of the dynamic model.
Another benefit of the dynamic model is that unlike the static model, it is not sensitive to
changes in the offset level of the load. Also, it does not need information on which time of the
year or day of the week it is. Hence, there is less risk for mistakes when handling the model.
The dynamic model will also partly adjust to changes in the system, through the use of
recently measured data in the differentiation of data by the model.
4.4 Return temperature model
To calculate the appropriate supply temperature from the predicted load, the return
temperature from the heat transfer needs to be known. In this project, quite a few ways of
estimating the return temperature has been tried. The estimate that worked out best was to
simply assume the future return temperature to be the same as the current return temperature.
The other methods of predicting the return temperature were black box modelling with daily
and weekly differentiation, black box modelling with only daily differentiation and static
linear modelling.
The return temperature depends on the outdoor temperature and the social load, as described
in chapter 2. It was rather simple to simulate for the period 2003-2004 using the daily and
weekly differential operator and an ARX model. However, in 2007, as well as in the future,
the return temperature is highly dependent on the cooling device “Beriden”, which bypasses
some water from the supply pipe to the return pipe, and then cools the return water. The
temperature of the return water before the bypass should correspond with the return
temperature predicted by the model for the network without the cooling device.
Unfortunately, this temperature is unknown. The only known parameters are the temperatures
immediately before and after the cooling device, the openness of the bypass valve and the
pressure on the supply and return line. To calculate the return temperature before the bypass
from this data would not be trivial.
However, “Beriden” is mostly used when the heat demand is modest and the flow on the net
is low, and in those cases the supply temperature is more or less constant since it has to ensure
the temperature of the tap water throughout the network, but not supply much heat for the
radiator systems. In fact, for all outdoor temperatures higher than +5°C, the supply
temperature is 75°C with the old control system. To evaluate that lower limit of the supply
temperature is outside the scope of this study. Therefore, there is only a need to estimate the
return temperatures for the cases when it is colder than +5°C, in which case the cooling
device is usually turned off, and the system is working as in the years 2003-2004. However,
since the outdoor temperature is often oscillating around +5°C, the model will be disturbed by
the transients from turning “Beriden” on and off. The method of differentiation of the signal
with the values from a day and a week ago makes the problems with disturbance extensive.
Even with only the daily differentiation, the problems are severe.
42
With the approach described above, one is trying to estimate the return temperature from the
load of the heat customers without the cooling. Since this is the load that the load model is
estimating, it seems like a straight forward method to use the return temperature from the
customers rather than the manipulated return temperature when calculating what supply
temperature is needed to meet their demand. The system is then modelled without the cooler.
Holding on to this approach, it was also tried to predict the return temperature with a static
linear model, neglecting the social factor. A first order polynomial was estimated for the part
of the data where the outdoor temperature is below 5°C, and the return temperature is
increasing with decreasing outdoor temperature (see Figure 12 in Chapter 3). This method
worked better than the methods using differentiation.
However, another approach to the return temperature is possible. If the cooling power is
added to the heat load of the customers, the return temperature after the cooling can be used to
calculate the appropriate control point of the supply temperature. The drawback here is that
this return temperature is following the pattern of the customer heat load when the cooling
device is turned off and another dynamic depending on the operation of the cooler when it is
turned on. When “Beriden” is in operation, the return temperature is rather stable. However,
“Beriden” is not used constantly but turned on and off frequently, and is changing both the
load and the return temperature in a step-like way compared to the slow dynamics of the rest
of the system. Still, the best estimate for the return temperature that has been found in this
project is simply assuming it to be equal to the last measured value, filtered through a mean
filter to reduce the noise.
The second approach, including the cooler in the model, also has the advantage that it can
handle situations when heat is cooled away to such an extent that the supply temperature has
to be increased.
43
5 Control strategies
In this chapter, feed forward control with the models described in Chapter 4 is compared to
feed forward with the present control curve. The characteristics of the supply temperature and
flow dynamics are described, and an assessment of the potential profit from implementing the
dynamic model is made.
In Figure 26, the old control system is sketched. The outdoor temperature Tout determines the
control point of the supply temperature TS,CP through the control curve (Figure 5 in Chapter
3). Depending on the load of the district heating system, there will be a resulting mass flow
m out from and in to the heat plant. If this flow is too big, the central pump will not be able to
keep up the pressure on the grid, and the substations in the periphery of the grid will
experience a lack of heat.
Figure 26. Block diagram of the old control of the supply temperature.
In Figure 27, the new control system can be seen. The outdoor temperature and measured
values of operational parameters are used to determine a control point for the supply
temperature using the dynamic model described in Chapter 4. This calculation is described in
detail in section 5.1. Again, the mass flow out from and in to the heat plant will be a result of
how well the model corresponds with the real system. If the model was perfect, the mass flow
would be constant for all supply temperatures over 75°C.
Figure 27. Block diagram of the new control of the supply temperature.
To compare the two control strategies, the supply temperature control point and the mass flow
needed to cover the heat demand using these supply temperatures during the validation
44
periods were calculated. The result is presented in section 5.2. The possible increase in
electricity production due to the lower supply temperature with the new control strategy is
assessed and valued in section 5.2.3 and 5.3.
5.1 Calculation of control point for the supply temperature
With the new control strategy, the control point of the supply temperature is calculated from
the prediction of the heat load, the prediction of the return temperature and a desired value of
the normal mass flow:
)ˆ(
)ˆ(ˆ)ˆ(ˆ)(,
ltmc
ltPktTtT
p
delRCPS
(38)
Where
TS,CP is the control point of the supply temperature
RT is the prediction of the return temperature
delP is the prediction of the heat load
cp is the specific heat capacity of water
m is the normal mass flow
The overall structure of the Simulink model used with the dynamic control strategy can be
seen in Figure 28. The supply temperature control point should be as low as possible, without
risking too high flows and thereby heat deficit in the DH system. The constant value of the
desired mass flow )ˆ( ltm must be chosen so that the margin is big enough for coping with
cases when the real heat load is bigger than the predicted heat load, or the return temperature
is higher than predicted. If the model is good, the flow variations will be small, and the
normal flow level can be set higher, and hence the supply temperature can generally be lower
without risking heat deficit on the grid.
Finally, the supply temperature control point signal is low pass filtered by a mean filter
calculating the mean value over the last five time steps. This is done to smooth out the supply
temperature control point signal and get rid of some of the noise from the load and return
temperature signals.
45
Figure 28. Block diagram of the simulink model structure. The upper left part of the model was described
in Chapter 4.2. Q is the volume flow of DH water out of from Idbäcken, m-dot is the corresponding mass
flow, TS is the measured supply temperature, TR is the measured return temperature, Tout is the outdoor
temperature and TScp is the control point for the supply temperature.
5.2 Comparison with the present control strategy
The evaluation of the new control strategy were done with a few different approaches. The
supply temperature and flow of the old and new control strategy were compared looking at
specific shorter time periods during high and medium load (at low loads, the new control does
not differ from the old one). The interaction between the heat load, supply temperature, flow
and return temperature was also analysed. This is presented in Chapter 5.2.1 and 5.2.2.
Looking at a longer period, the potential for a lower supply temperature in general with the
new control was assessed, and the risk of heat deficit on the grid with the old and new control
was compared. This is presented in Chapter 5.2.3.
5.2.1 High load case The high load case is exemplified with a few days in February, when the load is around 75
MW (the same time period that exemplified the dynamic load model validation in Chapter
4.2.4). In Figure 29, the supply temperature suggested by the dynamic model is compared to
the supply temperature suggested by the present control curve. Comparison of this graph with
the resulting flow presented in Figure 30 reveals that the new supply temperature is better
adjusted to keep up the flow of the system, but that the dynamic model has some problems,
mostly with overestimation of the load. However, the big dip in flow the 20th
of February is
avoided with the new control strategy, and in general the flow dips are shorter. It is also worth
noting that the flow dips with the new control strategy occur later in the morning. In fact, the
flow seems to make at dip during high load rather than during low load. This points to a
46
general overestimation of either the load or the return temperature during the morning load
peaks, and hence an unnecessarily high supply temperature at these times.
Figure 29. Comparison of the control strategies: Supply temperature, high load case, February 2007.
Figure 30. Comparison of the control strategies: Flow, high load case, February 2007.
Looking at Figure 31, where the calculated flow using the new control strategy is plotted
together with the new supply temperature, the load and the return temperature, one can
conclude that there is indeed an overestimation of the return temperature. The return
temperature is “predicted” to be the same as the last measurement of the return temperature,
so when the return temperature decreases, the prediction will be too high. In the cases when
47
the external cooling device “Beriden” is not in operation, the return temperature follows a
daily pattern, decreasing during the morning peak of the load. This results in a daily
overestimation of the return temperature, and hence a dip in flow and too high a peak in
supply temperature. These problems are due to the difficulty in modelling the return
temperature described in Chapter 4.4. Please note that the heat load and flow are scaled to fit
nicely in the picture, so only the timing of the parameters should be studied here, not the
magnitudes.
Figure 31. Result of new control strategy, high load case, February 2007. Flow and heat load are scaled to
fit the figure better.
5.2.2 Medium load case The medium load case is exemplified by a few days in the beginning of April 2007 (see also
Chapter 4.2.4). As can be seen in Figure 32 and Figure 33, the supply temperature is generally
lower and the flow higher than with the old control. Around 12 o’clock the 7th
of April, the
flow level is over 2000 t/h, which means that customers in the distant parts of the grid might
experience cold radiators. This high flow is due to the model’s failure to predict the load peak
at this time. The bad load prediction is probably due to the fact that the 7th
of April is the
Easter Saturday 2007.
48
Figure 32. Comparison of the control strategies: Supply temperature, medium load case, April 2007.
Figure 33. Comparison of the control strategies: Flow, medium load case, April 2007.
In Figure 34, the interaction of the flow, supply temperature, heat load, return temperature and
additional cooling for this load case can be seen. During the flow peak the 7th
of April, the
return temperature is decreasing rapidly when the cooler is started. The cooler is started
during an unusually high and late morning peak of the load, which adds to the high flow level.
If the load model had had information on the starting of the cooler in advance, it might have
been able to avoid this situation by increasing the supply temperature more. But since the
49
cooler is turned on and off manually based the electricity prices, this information is not easily
available.
Figure 34. Result of new control strategy, medium load case, April 2007. Flow and heat load are scaled to
fit the figure better.
5.2.3 Long term comparison To compare the two control strategies quantitatively, the potential increase in electricity
production and the risk of heat deficit on the district heating network were assessed for the
whole validation period February to May and September to December 2007.
The increase in electricity production was estimated as follows: For each time step, the
difference between the supply temperature with the old and the new control strategy was
calculated. Then the change in electric power was calculated according to the relation
between supply temperature and -value, derived in chapter 3:
ST0017.0 (39)
The relation between supply temperature and electric power production is thus
)()(0017.0)( tPtTtP heatSel (40)
The change in electricity production can then be calculated by integrating the change in
electric power over time. This was made by simply summing up the differences and
multiplying with the sample time, 1/6 h. The result from this calculation is presented in Figure
35 and Figure 36.
50
For comparison of the control system’s ability to meet the heat demand at all times, the
calculations of the needed flow was used. Since the limit of the flow according to the line of
argument in Chapter 3 seems to be 2100 t/h, the number of times the different control
strategies resulted in such high flows was counted, as well as for how long time such high
flows was needed to meet the load. This was used as a measure of the risk for heat deficit on
the grid with the different control strategies. Also, the number of times the flow would have to
be over 2000 t/h was counted. For these cases, there is a risk for heat deficit, even though it is
not as probable as for flows of 2100 t/h. However, if such high flows are only needed for a
short time, the heat deficit will probably not be noticed by the customers. Also, there might be
noise and outliers in the signals, giving stray high flow values. Therefore, the occations when
the flow would be high for less than three samples (half an hour) were removed. The result is
presented in Figure 35 and Figure 36, comparing the result for the old control strategy, the
new control strategy without outdoor temperature prognosis and the new control strategy
using temperature prognosis (real future values of the outdoor temperature was used as
temperature prognosis). The first (blue) bar shows half the increase in electricity production
for the whole validation period. The second (red) bar shows the number of samples for which
the flow would need to be over 2000 t/h for more than half an hour to meet the heat demand,
and the third (green) bar shows for how many samples the flow would need to be over 2100
t/h. In Figure 35, the normal flow in the model is 1750 t/h, whilst it in Figure 36 is 1700 t/h.
Of course, the higher normal flow, the lower the supply temperature can be and the higher is
the risk of heat deficit due to high flows. These things have to be weighed against each other.
Figure 35. Comparison of the control strategies over the time period February to May and September to
December 2007, with the normal flow 1750 t/h. The blue bar is half the increase in electricity production
with the new control compared to the old control. The red and green bar represents the risk of heat deficit
with the different control strategies.
51
Figure 36. Comparison of the control strategies when the normal flow is 1700 t/h, all other same as in
Figure 35.
As seen in Figure 35 and Figure 36, the lower flow level is appropriate if one wants to be sure
that the risk for heat deficit is not higher than with the old control strategy. This would give an
increase in the electricity production of the CHP plant with about 320 MWh. However, there
is reason to suspect that the flow variations will in fact be smaller with the new control
strategy than the model predicts, since the load in the model is approximated as a point load,
which enhances the variations compared to an equally spread load [1]. If this is the case, the
flow level could be increased to the higher level, and the electricity production would increase
with about 440 MWh.
It might also be interesting to see how the increased electricity production with the new
control strategy is distributed over the year. This is shown in Figure 37. The increase in
electricity production is bigger in the winter months, and this increase is emphasised with a
higher flow level. This is partly expected because the heat production is higher during the
winter, and hence a higher α-value will have more impact. On the other hand, one could also
expect that the supply temperature could not be decreased much during the colder months of
the year, compared the periods with medium load. In the warmest months, the new control
strategy does not change the electricity production much, since the supply temperature has its
default value 75°C most of the time.
52
Figure 37. Increase of electricity production per day during different months with the new control
strategy and two different flow levels.
If the increase in electricity production per day in January is assumed to be a mean value of
the increased electricity production per day in February, November and December, the extra
production for a whole year is 390 MWh for the low flow level or 540 MWh for the high flow
level.
5.3 Economy
To calculate the economical benefit of using the dynamic control strategy compared to the
one used today, it was assumed that the heat production and the efficiencies of the CHP-plants
would be the same, but the electricity production and hence the fuel consumption would
change. Since the change of the electricity production is due to a higher α-value, the
electricity production is increasing while the heat production is constant. The overall plant
efficiency is 85%, which means that for each extra produced MWh electricity, 1.18 MWh
more fuel would be used.
)85.0
1( fuelelel CCtPI (41)
where
I is the change in income in SEK
Pel is the change in electric power production in MW
t is the operation time in hours
Cel is the price of electricity, including green certificates, per SEK/MWh
Cfuel is the price of fuel per SEK/MWh
For the CHP plant Idbäcken, the fuel prices are 60-200 SEK/MWh, and the price for the sold
electricity is 400-500 SEK/MWh plus 200 SEK/MWh for green certificates. The extra income
from a decreased supply temperature will thus be between 35 and 60 SEK/ h at full heat load
(58 MW).
53
The extra profit from using the new control strategy would have been between 150 000 and
250 000 SEK for the year 2007 depending on fuel and electricity prices, if the lower flow
level was used. The daily profit increase would be 900-1500 SEK for a winter day and 500-
800 SEK for a spring or autumn day.
If the higher flow level could be used, the increased income for a year would be between
200 000 and 350 000 SEK, and daily it would be 1400-2200 SEK in winter and 600-900 SEK
in spring and autumn.
5.4 Implementation
The model can be implemented at the CHP plant Idbäcken through an external computer that
would use logged process data to calculate a control point for the supply temperature. This
value can be fed to the present control system through an already existing input port for an
external control signal.
If the model is implemented, it can be evaluated properly after having run for some time, and
the flow level of the model can be adjusted. The flows calculated by the model could easily be
compared with the actual measured flows, to give an indication on how accurately the model
is working.
54
6 Discussion
The aim of this project was to investigate the possibilities to decrease the supply temperature
of the district heating network in Nyköping by using weather forecasts and dynamic methods.
Attempts to use data on wind speed and solar irradiation was not fruitful, but a prognosis on
the outdoor temperature turned out to be of some use. The main method to set the control
point of the supply temperature was to predict the load using differentiation with respect to
the daily variations and a simple black box model with the outdoor temperature as input
signal. Various methods were tried to model the return temperature, but in the end the best
estimation was the last measured value. The main obstacle in the return temperature
modelling process was how to handle the impact on the system of the external cooling device
“Beriden”.
6.1 Input signals
The input signals used to predict the load on the district heating system was outdoor
temperature measured at the heat plant, wind speed measured at Skavsta Airport outside
Nyköping and global solar irradiation at Nyköping modelled by SMHI from measured data at
some locations around Sweden. As outdoor temperature prognosis, known future values were
used. It can therefore be expected that the models using the temperature prognosis will not
give as accurate results as they did in the modelling process, since there will be some error in
the prognosis.
Concerning the fact that the wind speed and solar irradiation was not improving the models,
there can be some different reasons for this. The data might not be accurate enough to give
good results. For example, the wind speed at Skavsta might not correspond enough with the
local wind speeds at the buildings using district heating in Nyköping. Some part of both the
wind speed variations and especially the solar irradiation is season dependent or depends on
the time of the day, and will be modelled automatically by the differentiation of the input and
output signals in the model. The cross correlation between the load and the wind speed and
solar irradiation respectively is low, and this also indicates that these signals are not useful to
predict the load.
SMHI has recently introduced a new service called Energy Index. The energy index is a
parameter that describes the impact of the weather conditions on the heating need of a specific
building or a specific area. It weighs together temperature, solar irradiation, winds and
precipitation to an equivalent temperature. It has not been possible to use this parameter in the
modelling process in this degree project, since SMHI did not have calculations of the energy
index with the high resolution (10 minutes sample time) that would have been needed to use it
in this model. Today, they calculate daily and monthly values of the energy index. However,
SMHI are interested in cooperation with energy companies around this, and could provide
data with higher resolution if they were involved in a project from scratch.
6.2 Possible improvements
The model can be improved in several ways. First of all, the performance would be better if
the return temperature could be modelled more accurately. Preferably, if the return
55
temperature could be measured before the bypass from the supply line to the cooling device
“Beriden”, predictions of the unaffected return temperature could be made. This temperature
is easier to model, and hence the predictions of it should be better. Without this measurement,
some improvement might be possible if two parallel models of the return temperature were
used, one for cases when “Beriden” is running and one for cases when there is no external
cooling. This could improve the predictions especially during the cold months, when a
reduced supply temperature is most profitable. Another important improvement would be to
somehow give the model information in advance when the operation of “Beriden” is changed.
Then the load predictions could be more accurate, and also the switch between the different
return temperature models could be smoother. However, this would demand that either the
operation of “Beriden” would be automatized, or that the operator manually inputs an
operation plan to the model.
The district heating network is connected to a 10 000 m3 accumulator tank. This tank has not
been included in the model. The tank is used to even out the heat production during the day,
and it could be interesting to analyse strategies for this together with the strategies for the
supply temperature.
6.3 Drawbacks and benefits
The main benefit of the control strategy suggested in this project is a better electricity
efficiency of the Idbäcken CHP plant. This efficiency improvement would lead directly to an
increased electricity production and hence a higher income. Even though 200 000 SEK/year is
not a very big amount of money, the effort could be beneficial since it is simple and cheap to
make. Also, there are good chances that the suggested control strategy could be improved if it
was tried out on the plant. A positive side effect of the lower supply temperature with the
suggested control strategy is that it would also reduce the heat losses from the district heating
pipes to the ground.
In the ideal case, when the model can predict the load and return temperature correctly, the
flow on the district heating network would be more stable than with the old control strategy.
This stability can be used to tighten the margin of the system, generally decreasing the supply
temperature. It can also be used to reduce the need for increasing the capacity of the grid
when new customers are connected. This could save a lot of investment money under such
circumstances.
A possible drawback of the suggested control strategy is the increased variations of the supply
temperature. These might result in stress on the pipe system, leading to leaks or other
problems that would demand more maintenance on the district heating grid. How the costs
due to wear on the pipes compares to the incomes from the extra electricity production from
using the presented control strategy should maybe be investigated before implementing it.
56
7 References
7.1 Litterature
[1] Larsson G. Dynamik i fjärrvärmesystem. Göteborg: Department of Thermo and Fluid
Dynamics, Chalmers University of Technology; 1999.
[2] Alvarez H. Energiteknik. Lund: Studentlitteratur; 2003.
[3] Ekroth I., Granryd E. Tillämpad termodynamik.Stockolm: Institutionen för
Energiteknink, Avdelningen för tillämpad termodynamik och kylteknik, Kungliga
tekniska högskolan; 1994.
[4] Fredriksen S, Werner S. Fjärrvärme - teori, teknik och funktion. Lund:
Studentlitteratur; 1993.
[5] Larsen H., Bøhm B., Wigbels M. A comparison of aggregated models for simulation
and operational optimisation of district heating networks. Energy Conversion and
Management, 45; 2004.
[6] Kvarnström J., Dotzauer E., Dahlquist E. Produktions- och distributionsplanering av
Fjärrvärme. Stockholm: Värmeforsk rapport 990; 2006.
[7] Glad T., Ljung L. Reglerteknik. Grundläggande teori. Lund: Studentlitteratur; 1989.
[8] Glad T., Ljung L. Modellbygge och simulering. Lund: Studentlitteratur; 1989.
[9] Kailath T., Sayed A., Hassibi B. Linear Estimation. Prentice Hall Information and
System Sciences Series; 2000.
[10] Carlsson B. Empirical Modelling of Energy Processes - Project Description within the
course Empirical Modelling at Uppsala University 2007. Uppsala University,
Department of Systems and control; 2007.
[11] Gabrielaitiene I., Bøhm B., Sunden B. Modelling temperature dynamics of a district
heating system in Naestved, Denmark – A case study. Energy Conversion and
Management 48; 2007, p 78-86.
[13] Keppo I., Ahtila P. Optimering av fjärrvärmevattnets framledningstemperatur i mindre
fjärrvärmesystem. Svenska fjärrvärmeföreningens Service AB rapport 2002:6; 2002.
[14] Larrson G. Flödesutjämnande körstrategi. Svenska Fjärrvärmeföreningens Service AB
rapport 2003:86; 2003.
[15] Johnsson J., Rossling O. Samverkande produktions- och distributionsmodeller.
Svenska Fjärrvärmeföreningens Service AB rapport 2003:83; 2003.
[16] Hedin K. En flödesutjämnande driftstrategi för Uppsalas fjärrvärmesystem. En ändrad
styrning av framtemperaturen. Examensarbete. Uppsala Universitet, teknisk- och
naturvetenskaplig fakultet; 2006.
[17] Dotzauer E. Simple model for prediction of loads in district-heating systems. Applied
Energy 73; 2002, p 277-284.
[18] Johansson A. Fault Detection of Hourly Measurements in District Heat and Electricity
Consumption. Examensarbete. Linköping: Linköpings tekniska högskola, Department
of Electrical Engineering; 2005.
[19] Malmström B., Nilsson D., Vallgren H. Korttidsprognoser för fjärrvärmelast och
utetemperatur med on-linekopplade datorer. Stockholm: Värmeforsk rapport
589;1996.
[20] Felix R. Prediktion av elförbrukning med periodiska styckvis linjära modeller.
Examensarbete. Chalmers tekniska högskola och Lunds tekniska högskola; 1997. [21] Jansson L-E. Metoder för ökat elutbyte i befintliga hetvattenanläggningar. Stockholm:
Värmeforsk rapport 619; 1997.
57
[22] Axby F., Johansson I., Måfält M., Ifwer K., Svensson N., Öhrström A. Mer El!
Metodisk genomgång av befintliga anläggningar. Stockholm: Värmeforsk rapport 985;
2006.
7.2 Data
[23] Process data from the process data base of the CHP plant Idbäcken in Nyköping,
average values with sample time 10 minutes.
[24] STRÅNG data used here are from the Swedish Meteorological and Hydrological
Institute (SMHI), and were produced with support from the Swedish Radiation
Protection Authority and the Swedish Environmental Agency.
[25] Wind data from Swedish Meteorological and Hydrological Institute (SMHI),
measurements at Skavsta, Nyköping’s Airport. Sample time was 30 minutes.
7.3 Other
[12] Private conversation with Majjid Mohammadi, Vattenfall Värme Norden, Uppsala.
A1
Appendix 1: The simulink model
100Delays
memory1
100Delays
memory
volumeFlow
measured volumeflow U
E1
U(E)
delay of load
100Delays
Tapped Delay1
simGammalTS
Supply temp with old control
simLast
Simulated load(t)Prediction horizon
simTS
Output supply temp with new control
temp
Outdoor temp
simMdotOldC
Old control mass flow (t-l)
Old control curve
simMdot
New control mass flow (t-l)
TS
Measured supply temp
TR
Measured return temp
massFlow
Measured massflow last
Tout
transport time l
prediction horizon
Toutprog
modelled load
Load modeltempProg
FromWorkspaceMATLAB
FunctionEstimation of lhat
cool
Cooling
TR
modelled load
TS
Calculation of supply tempTRTSmassf low (t/h)l
load (MW)
Calculation of previous load
MATLABFunction
Calculation of l
MATLABFunction
Calculation of k
TR
last
k
TS
mass f low
Calculation of flow with present control
k
TR
last
TS
mass f low
Calculation of flow with new control
Add2
Add
Figure 1, Overview of simulink model
A2
1load (MW)
simm
time m
-K-
mult by Cp andunit conversion
h to s
U
E1
U(E)
mdot(t-m)
100Delays
Tapped Delay1
100Delays
Tapped Delay
U
E1
U(E)
TS(t-2deltat)
simcalcLoad
Real load
2
Gain
Divide
Add
4m
3massflow (t/h)
2TS
1TR
Figure 2, Calculation of previous load
A3
1modelled load
Toutprog
Tout
last
predHorizon
l
x
y
x1
loadpred
load predictor1
z
1
Unit Delay
simToutdiff
To Workspace2
simPredHorizon
To Workspace1
simLastAntiDiff
To Workspace
100Delays
Tapped Delay1
100Delays
Tapped Delay
simLastOkyld
Simulated load excluding cooling power
prediction horizon
last1
transport time l
add to rev erse dif f erentiation
Reversed differentiation of load
-K-
Gain1
-K-
Gain
transport time l
last
lastdif f
Differentiation of load
-576Z
Delay day7
-432Z
Delay day6
-288Z
Delay day5
-144Z
Delay day4
-576Z
Delay day3
-432Z
Delay day2
-288Z
Delay day1
-144Z
Delay day
Add4
Add3
Add2
Add1
Add
5Toutprog
4prediction horizon
3transport time l
2Tout
1last
Figure 3, Load model
A4
1lastdiff
1500Delays
Tapped Delay4
1500Delays
Tapped Delay3
1500Delays
Tapped Delay2
1500Delays
Tapped Delay1
U
E1
U(E)
Selector4
U
E1
U(E)
Selector3
U
E1
U(E)
Selector2
U
E1
U(E)
Selector1
-576Z
Integer Delay3
-432Z
Integer Delay2
-288Z
Integer Delay1
-144Z
Integer Delay
-K-
Gain
576
Constant4
144
Constant3
432
Constant2
288
Constant1
Add8
Add7
Add6
Add5
Add4
Add3
Add2
Add1
Add
2last
1transport time l
Figure 4, Differentiation of load signal
A5
1add to reverse differentiation
1500Delays
Tapped Delay8
1500Delays
Tapped Delay7
1500Delays
Tapped Delay6
1500Delays
Tapped Delay5
1500Delays
Tapped Delay4
1500Delays
Tapped Delay3
1500Delays
Tapped Delay2
1500Delays
Tapped Delay1
U
E1
U(E)
Selector8
U
E1
U(E)
Selector7
U
E1
U(E)
Selector6
U
E1
U(E)
Selector5
U
E1
U(E)
Selector4
U
E1
U(E)
Selector3
U
E1
U(E)
Selector2
U
E1
U(E)
Selector1
-K-
Gain
576
Constant8
576
Constant7
432
Constant6
432
Constant5
144
Constant4
288
Constant3
288
Constant2
144
Constant1
Add8
Add7
Add6
Add5
Add4
Add3
Add2
Add1
Add
3transport time l
2last1
1prediction horizon
A6
Figure 5, Reversed differentiation of load
1TS
TS TSmeanfi lter
mean filter
1700
desired flow
4Delays
Tapped Delay Saturation-K-
Divide by cp and unit converison
Divide Add2modelled load
1TR
Figure 6, Calculation of supply temperature control point
1mass flow
simTScomp
supply temp associatedto load and flow
simTR
return temp 100
Delays
Tapped Delay2
100Delays
Tapped Delay1
U
E1
U(E)
Selector2
U
E1
U(E)
Selector1
-K-
Gain
Divide
Add1
simTRcomp
"modelled return temp"
4TS
3last
2TR
1k
Figure 7, Calculation of flow with new control
A7
Appendix 2: Matlab functions for calculation of transport times k, l and lhat
2.1 Calculation of l: function[deltat]= transportTime(Q)
%transportTime beräknar transporttiden från värmeverket till lasten % Q är en vektor med nyaste flödena först
V1=4000; deltat=0; V=0; i=100; while V<V1 && deltat<49 deltat=deltat+1; V=V+Q(i)/6; i=i-1; end
2.2 Calculation of k: function[deltat]= transportTime2(Q)
%transportTime2 beräknar transporttiden tur och retur värmeverk-last
V1=8000; deltat=0; V=0; i=100; while V<V1 && deltat<49 deltat=deltat+1; V=V+Q(i)/6; i=i-1; end
2.3 Calculation of lhat: function[deltat]= transportTimeForward(Q)
%transportTimeForward skattar framtida transporttiden för framledningsvattnet
från värmeverket till lasttyngdpunkten. Flödet den närmaste framtiden antas %vara lika stort som medelvärdet av flödet den senaste timmen. % Q är en vektor med nyaste flödena först
V1=4000; Qnow=mean(Q(1:6)); deltat=round(V1/Qnow*6); if deltat>49 deltat=49; end
A8
Appendix 3: Matlab functions for load prediction
3.1 Embedded matlab function “Load predictor” in the simulink model function [y, x1] = loadpred(Toutprog,Tout,last,predHorizon,l,x)
y0=last; k=1; u=zeros(100,1); %u ska vara en vektor med insignaler från tiden t till
tiden t+100. %Insignalerna är kända fram till tiden t+deltat. for j=1:l u(j)=Tout(100-l+j); end for i=(l+1):100
u(i)=Toutprog(k); %för tidpunkter när insignalen är okänd sätts den
till det senaste kända värdet, Tout(100) k=k+1; end
H=[0.96,-0.021,0.0296,-0.5358,0.0307,0.4352;]; F=[0.96,-0.021,0.0296,-0.5358,0.0307,0.4352;1,0,0,0,0,0;
0,1,0,0,0,0;0,0,0,0,0,0;0,0,0,1,0,0;0,0,0,0,1,0;]; G=[0;0;0;1;0;0;]; K=[1;0;0;0;0;0;]; matris=[.....]; %matrix created by the code in “The predictor”, see below
gamma=F-K*H;
%prediktera yt=zeros(100,1); for i =1:100 yt(i)=H*F^(i-1)*gamma*x+matris(i,:)*u+H*F^(i-1)*K*y0; end
y=yt(predHorizon);
%modellfelet i förra steget e=y0-H*x;
%nytt tillstånd: x1=F*x+G*u(1)+K*e;
3.2 Matlab code for creating the vectors and matrix to the “Load predictor”: %prediktor för lastprediktion
clear all load lastArxMean4 %the ARX model
na=length(lastArx.A)-1;
A9
nb=length(lastArx.B);
%H-vektorn: H=[-lastArx.A(2:(na+1)) lastArx.B];
%F-matrisen: matA1=eye((na-1),(na)); matB1=zeros((na-1),(nb)); matA2=zeros((nb),na); matB2=[zeros(1,(nb)); eye(((nb-1)),(nb))];
F=[H; [matA1 matB1]; [matA2 matB2]];
%G-vektorn: G=zeros(na+nb,1); G(na+1)=1;
%K-vektorn K=eye((na+nb),1);
%prediktion: gamma=F-K*H;
%skapa matris för prediktion med 100 prediktioner
matris=zeros(100,100); for i=1:100 j=1; while j<=i matris(i,j)=H*F^(i-j)*G; j=j+1; end end
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